Making edges render with Cycles
The laplacian Lightning generator produces a set of Mesh objects. At its most basic setting, using two empties (origin and ground). 



You can use the Single Mesh tickbox to make sure it's all one mesh, you lose flexibility, but the sake of example that method is probably handiest.




You can add a skin modifier to the mesh. By default the skinned edges is probably not the right size, you enter edit mode on the mesh, and go to vertex selection mode, select all vertices, then ctrl+a to scale down the radius of the skin.
Alternatively convert it to a Curve object (it will convert each edge to a straight section Curve type)  (alt+C > Curve From Mesh)


Both solutions will render fine in Cycles.



For the animation, perhaps you might use a Build Modifier and tick reverse. Remember Light is a really fast phenomenum, often all we see is the trail of air burning and extinguishing rather fast.

Ultra Slowmotion: 



I think it might have been better to subdivide the generated mesh a few times..now it exhibits jumps.. 

Credits to gandalf3 for this one:



Alternatively

(unless you need to generate a tonne of different strikes) Why not trace a photograph and use artistic discretion to 3d spatialize it, and animate that strike:)